Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}3x+7y &= -3 \\ 5x+5y &= 5\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $5x = -5y+5$ Divide both sides by $5$ to isolate $x$ $x = {-y + 1}$ Substitute this expression for $x$ in the first equation. $3({-y + 1}) + 7y = -3$ $-3y + 3 + 7y = -3$ Simplify by combining terms, then solve for $y$ $4y + 3 = -3$ $4y = -6$ $y = -\dfrac{3}{2}$ Substitute $-\dfrac{3}{2}$ for $y$ in the top equation. $3x+7( -\dfrac{3}{2}) = -3$ $3x-\dfrac{21}{2} = -3$ $3x = \dfrac{15}{2}$ $x = \dfrac{5}{2}$ The solution is $\enspace x = \dfrac{5}{2}, \enspace y = -\dfrac{3}{2}$.